theorem
  s1 is_next_of s0 & s2 is_next_of s1 & H in the LTLold of s1 & H is
  Until implies the_right_argument_of H in the LTLold of s1 or
  the_left_argument_of H in the LTLold of s1 & H in the LTLold of s2
proof
  assume that
A1: s1 is_next_of s0 & s2 is_next_of s1 & H in the LTLold of s1 and
A2: H is Until;
  set G = the_right_argument_of H;
  set F = the_left_argument_of H;
  H = F 'U' G by A2,MODELC_2:8;
  hence thesis by A1,Lm29;
end;
